Category: 3. Business

Meta CEO Mark Zuckerberg is making big change to its AI operations for which he has hired execs at $100 million-plus packages; read memo
In a new and dramatic move, Meta CEO Mark Zuckerberg is making the most aggressive move in his AI arm race. Zuckerberg is now reorganising the company’s artificial intelligence operations by restricting the Meta Superintelligence Labs (MSL) into four distinct teams. As reported by Business Insider the company outlined the move in an internal memo from the newly appointed chief of AI Alexandr Wang. The restructuring is taking place after the aggressive hiring process in which Meta poached dozens of top AI researchers from its rivals companies. The internal email, sent by Alexandr Wang, the 28-year-old head of Meta Superintelligence Labs (MSL), outlines a dramatic restructuring aimed at accelerating Meta’s pursuit of “personal superintelligence”—AI that can outperform humans across intellectual domains.

Four pillars of Meta’s new AI strategy

In the internal memo shared with employees, Wang talks about the four specialised teams:
TBD Lab: This is a small elite unit that will majorly focus on training and scaling large models, including a mysterious “omni” model.

FAIR: It is a research arm of Meta and now it will take care of feeding innovations directly into model training.

Products & Applied Research: This team will be led by ex-GitHub CEO Nat Friedman. The team will work on integrating AI into Meta’s consumer offerings.

MSL Infra: This team will be headed by engineering veteran Aparna Ramani and it will work on building the infrastructure needed to support cutting-edge AI development.
Most of these leaders now report directly to Wang, signaling a centralization of power within MSL.

FAIR and TBD: Meta’s innovation engine

FAIR, led by Rob Fergus and chief scientist Yann LeCun will now play an important role in the development of MSL’s model. Whereas, TBD Lab will look for new directions, including the enigmatic “omni” model—believed to be a multimodal system capable of understanding text, audio, video, and more.The research wing at MSL will be headed by Shengjia Zhao, co-creator of ChatGPT, who notably does not report directly to Wang.

Read Alexandr Wang’s full memo here

Superintelligence is coming, and in order to take it seriously, we need to organize around the key areas that will be critical to reach it — research, product and infra. We are building a world-class organization around these areas, and have brought in some incredible leaders to drive the work forward.

As we previously announced, Shengjia Zhao will direct our research efforts as Chief Scientist for MSL, Nat Friedman will lead our product effort and Rob Fergus will continue to lead FAIR. Today, I’m pleased to announce that Aparna Ramani will be moving over to MSL to lead the infrastructure necessary to support our ambitious research and product bets.

As part of this, we are dissolving the AGI Foundations organization and moving the talent from that team into the right areas. Teams whose work naturally aligns with and serves our products will move to Nat’s team. Some of the researchers will move to FAIR to double down on our long term research while teams working on infra will transition into Aparna’s org. Anyone who is changing teams will get an update from their manager or HRBP today, if you haven’t already.

We’re making three key changes to our organizational design that will help us to accelerate our efforts.
Centralizing core, fundamental research efforts in TBD Lab and FAIR.

Bolstering our product efforts with applied research that will work on product-focused models.

Establishing a unified, core infrastructure team to support our research bets.
The work will map to four teams:

TBD Lab will be a small team focused on training and scaling large models to achieve superintelligence across pre-training, reasoning, and post-training, and explore new directions such as an omni model.

FAIR will be an innovation engine for MSL and we will aim to integrate and scale many of the research ideas and projects from FAIR into the larger model runs conducted by TBD Lab. Rob will continue to lead FAIR and Yann will continue to serve as Chief Scientist for FAIR, with both reporting to me.

Products & Applied Research will bring our product-focused research efforts closer to product development. This will include teams previously working on Assistant, Voice, Media, Trust, Embodiment and Developer pillars in AI Tech. Nat will continue to lead this work reporting to me.

MSL Infra team will unify elements of Infra and MSL’s infrastructure teams into one. This team will focus on accelerating AI research and production by building advanced infrastructure, optimized GPU clusters, comprehensive environments, data infrastructure, and developer tools to support state-of-the-art research, products and AI development across Meta. Aparna will lead this team reporting to me.

Ahmad and Amir will continue reporting to me focusing on strategic MSL initiatives they will share more about later.

I recognize that org changes can be disruptive, but I truly believe that taking the time to get this structure right now will allow us to reach superintelligence with more velocity over the long term. We’re still working through updated rhythms and our collaboration model across teams, including when we’ll come together as a full MSL org.

Thank you all for your flexibility as we adapt to this new structure. Every team in MSL plays a critical role and I’m excited to get to work with all of you.
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August 23, 2025
The effect of food packaging color on calorie estimation in virtual reality

Obesity is a complex disease that not only affects an individual’s appearance but also has multifaceted negative impacts on physical health, including cardiovascular diseases, type 2 diabetes, hypertension, fatty liver disease, and certain types of cancer¹. Additionally, obesity contributes to psychological distress, increasing the risk of depression and anxiety, and imposes a significant economic burden on public health systems^2,3. Given the rising prevalence of obesity, understanding how consumers estimate food calories and make dietary choices is essential for both public health and marketing strategies. Previous research has strongly linked obesity with the underestimation of food calories, highlighting the need for interventions that help consumers make more informed choices^4,5,6.

Food choices are influenced by various factors, including economic conditions, sociocultural influences, psychological aspects, marketing strategies, and food packaging design^7,8,9. Among these, food packaging color plays a crucial role in shaping consumer perceptions and decision-making. Colors can act as implicit cues that influence caloric estimations, thereby affecting consumers’ food selections and dietary behaviors¹⁰. As a key element of sensory marketing, packaging color has the potential to nudge consumers toward healthier choices, making it a valuable tool for both businesses and policymakers.

Despite extensive research on food packaging and consumer behavior, there remains a significant research gap regarding how color influences calorie estimation and the mediating role of perceived healthiness in this relationship. Furthermore, most existing studies rely on self-reported surveys or controlled laboratory experiments, which may lack ecological validity. This study uses virtual reality technology to investigate how food packaging color (red vs. green) influences consumers’ calorie estimations and whether perceived healthiness mediates this effect. By uncovering these mechanisms, this research provides insights that are relevant not only to public health interventions but also to food industry marketing strategies and regulatory policies. Specifically, these findings can inform front-of-pack labeling regulations and guide food manufacturers in designing health-oriented packaging that encourages better consumer choices^11,12. Given the increasing emphasis on behavioral nudges in public policy, understanding the impact of color-coded cues on food perception can help develop more effective marketing and regulatory frameworks, ultimately contributing to obesity prevention and healthier consumer behavior.

Color, caloric estimation, and perceived healthiness

Color is one of the most immediate and influential visual cues in food packaging, shaping consumer perceptions and decision-making processes. Previous research has highlighted the significant impact of front-of-pack (FOP) visual cues on consumer food choices and eating behaviors, emphasizing the role of packaging color as a critical element in shaping dietary decisions¹³. Consumers frequently rely on packaging color to infer the healthiness and caloric content of food rather than consulting detailed nutritional labels^5,14,15. However, the specific mechanisms by which color affects food health perception and caloric estimation remain unclear, particularly regarding the mediating role of perceived healthiness in this relationship.

Food packaging color plays a crucial role in shaping consumer perceptions of healthiness. Research has shown that color-coded packaging influences consumer expectations about food attributes, often more strongly than textual nutritional information¹⁶. Green is typically associated with health, natural ingredients, and lower calories, whereas red is often linked to high-calorie, indulgent, and less healthy foods^17,18. These associations arise not only from everyday experiences but also from strategic marketing practices. Many health-oriented products use green packaging to emphasize their nutritional benefits, while high-calorie snacks or fast foods often employ red to attract attention and stimulate impulse purchases^19,20. Moreover, color influences sensory expectations, with red enhancing perceptions of richness and indulgence, whereas green can make food seem healthier but potentially less flavorful²¹. Recent research has expanded from examining singular color effects to investigating the interactions between color and other visual cues, such as shape and labeling²². Recent research by Hallez et al. (2023) further supports the significant role of packaging color in shaping consumer perceptions of healthiness, sustainability, and taste among young consumers. Their study demonstrates that color, in interaction with packaging claims, influences product evaluations, with findings closely aligning with the current research on color-driven health perceptions. This highlights the importance of considering interactive effects between color and other visual or textual cues in food packaging design, an area warranting further exploration in the context of calorie estimation²³. For example, Grunert & Wills (2007) found that consumers prefer simplified front-of-pack labeling formats but differ in their reliance on color-based health cues depending on the product category and context²⁴. However, the precise mechanisms by which color influences food health perception require further empirical validation.

Studies suggest that consumer perceptions of a food product’s healthiness significantly influence their caloric judgments²⁵. Prior research indicates that consumers tend to overestimate the caloric content of foods they perceive as unhealthy while underestimating those they deem healthy²⁵. This phenomenon has been observed in various contexts; for example, when consumers compare two identical yogurt products labeled as “low-fat” and “full-fat,” they consistently judge the full-fat yogurt as having higher calories, despite both products containing the same caloric content²⁶. Similarly, fast food consumers—especially those frequenting health-branded chains such as Subway—tend to underestimate the caloric content of meals, leading to higher caloric intake²⁷. In one study, participants were asked to evaluate the healthiness and caloric content of eight different foods. The results showed that foods perceived as healthy or beneficial for weight loss were typically underestimated in caloric content, whereas foods perceived as unhealthy or detrimental to weight loss were overestimated¹⁷. Furthermore, the health-oriented branding of a restaurant can lead consumers to underestimate the caloric content of its meals, resulting in increased caloric intake¹⁴. These findings indicate that consumers do not estimate calorie content directly based on the food itself but rather indirectly through their judgments of healthiness. Thus, food packaging color may first influence health perception, which in turn affects caloric estimation^19,20. While perceived healthiness has been widely studied in consumer decision-making, its specific mediating role in the color–caloric estimation relationship remains underexplored.

Overall, food packaging color may influence caloric estimation by first shaping consumers’ perceptions of healthiness. However, most existing research has focused on color’s impact on food choice and consumption behavior, with limited direct investigation into how color affects caloric estimation²². Additionally, prior studies have relied primarily on self-reported surveys or controlled laboratory experiments, which may lack ecological validity. With the development of Virtual Reality (VR) technology, this research integrates VR to further enrich and develop its application in consumer behavior studies. Compared to traditional research methodologies, VR technology offers low costs, reusability of experimental scenarios, and immersive experiences that more accurately replicate real-world environments²⁸, thereby holding significant advantages in consumer research. Therefore, this experiment leverages VR technology to perform experimental manipulations, aiming to explore the underlying mechanisms more profoundly.

Theoretical framework: association theory and embodied cognition theory

Sensory marketing research frequently utilizes Association Theory and Embodied Cognition Theory to explain how sensory cues influence consumer perceptions and behaviors. These theories provide a foundation for understanding how color cues (red vs. green) affect consumers’ calorie estimations through their perceptions of healthiness.

Association Theory posits that repeated co-occurrences of stimuli lead to learned associations, allowing consumers to anticipate one event based on the presence of another²⁹. In food packaging, red and green are commonly used in health-related messaging, shaping consumer expectations. Red is often associated with cautionary signals, energy, and intensity, while green is frequently linked to health, natural ingredients, and lower-calorie options. These learned associations influence consumer judgments, leading to expectations that green-packaged foods are healthier and lower in calories, whereas red-packaged foods may be perceived as less healthy and higher in calories. This heuristic processing may guide consumer decision-making, particularly in contexts where detailed nutritional information is not immediately considered.

Embodied Cognition Theory, in contrast, suggests that cognitive processes are deeply rooted in bodily interactions with the environment, meaning that sensory experiences—such as visual exposure to color—can directly shape cognitive evaluations and perceptions. Research has demonstrated that bodily perceptions significantly impact consumer experiences; for instance, tactile sensations influence service perception, with soft textures enhancing tolerance for service failures³⁰, while rough textures evoke empathy and generosity³¹. Similarly, product shape affects size perception, as consumers tend to perceive round pizzas as smaller than square pizzas of the same surface area³². In the context of food perception, color can elicit immediate cognitive and affective responses, influencing how consumers assess healthiness and caloric content. Red may enhance perceptions of higher energy content, whereas green may reinforce associations with health and lower caloric density.

By integrating Association Theory and Embodied Cognition Theory, this study examines how packaging color influences consumers’ calorie estimations through their perceptions of healthiness, providing insight into the cognitive mechanisms underlying food-related judgments.

Research objectives

This study aims to investigate how food packaging color (red vs. green) influences consumers’ calorie estimations and whether perceived healthiness mediates this effect. While previous research has demonstrated that color cues shape consumer perceptions, the underlying cognitive mechanisms—particularly the mediating role of perceived healthiness—remain underexplored. Drawing on Association Theory and Embodied Cognition Theory, this research seeks to clarify how learned associations (e.g., red with unhealthiness and green with health) and direct sensory experiences influence food-related judgments.

Specifically, this study examines whether red packaging leads to higher calorie estimations and green packaging leads to lower ones, particularly in the context of unhealthy foods. Since consumers often rely on heuristic cues, color may serve as a visual shortcut for evaluating a product’s healthiness, subsequently influencing calorie estimation. However, if the association between color and healthiness is disrupted—such as through an experimental manipulation where color is framed as unrelated to health—the effect of color on calorie estimation should diminish. Additionally, this research explores whether altering the color-health association affects consumers’ food choices, potentially leading to an increase in food selection when color no longer serves as a heuristic signal for health.

To address these research objectives, the following hypotheses are proposed:

H1: For unhealthy foods, red packaging will increase consumer calorie estimations compared to green packaging.

H2: Perceived healthiness mediates the effect of packaging color on calorie estimation of unhealthy foods.

H3: For unhealthy foods, the association of red with unhealthiness will lead to higher calorie estimations of foods in red packaging. After manipulating “color unrelated to health,” the impact of color on calorie estimation will disappear in the manipulated group.

H4: Compared to the control group, the number of food choices will increase in the manipulated group where “color is unrelated to health.”

By testing these hypotheses, this study seeks to provide both theoretical contributions to sensory marketing and practical implications for food packaging design and public health communication. Understanding how color influences calorie estimation through perceived healthiness can inform strategies for promoting healthier eating behaviors and improving consumer awareness of nutritional content.

Study 1: the impact of food packaging color on calorie Estimation

Study 1 employs a single-factor between-subjects design, with the independent variable being packaging color, divided into two levels: red and green. The dependent variable is the numerical estimation of calories, and the mediating variable is the perceived level of healthiness.

Experimental objectives and hypotheses

The purpose of Study 1 is to explore the impact of food packaging color on calorie estimation and to examine the mediating mechanism of perceived healthiness. The following hypotheses are proposed for this experiment:

H1: For unhealthy foods, red packaging will increase calorie estimations compared to green packaging.

H2: Perceived healthiness mediates the effect of packaging color on calorie estimation for unhealthy foods.

Participants

Participants were recruited through the distribution of a survey link on social media platforms using Questionnaire Star. A total of 159 respondents completed the survey, including 67 males and 92 females, with an age range of 18–32 years (M = 23.55, SD = 2.46). The studies involving human participants were reviewed and approved by Fudan University Ethics Committee (FDU-SSDPP-IRB-2024-2-103). They were performed by the ethical standards laid down in the 1964 Declaration of Helsinki and its later amendments. All participants in the study provided informed consent, which involves the consent to publish their data.

Experimental materials

Food packaging images

Following previous studies, the products were categorized into two broad categories: healthy and unhealthy, with a total of six products selected (see Appendix 1).

This design allows for a controlled and focused examination of the influence of color on perceived calorie content, leveraging both visual stimuli and participant self-report measures to gather data on perception dynamics influenced by packaging color (see Fig. 1).

Fig. 1

Example of product images (red on the left and green on the right).

Healthy categories include yogurt, nuts, and fruit cereal, while unhealthy categories include potato chips, chocolate, and milk tea instant beverages. These six products were processed through Photoshop, keeping all aspects identical except for the packaging color. To maintain consistency, the RGB color values for red are: Red: 213; Green: 32; Blue: 53. The RGB color values for green are: Red: 123; Green: 225; Blue: 47.

To exclude other possible explanations such as taste appeal and attractiveness of packaging, participants were required to evaluate the taste appeal of the food, the attractiveness of the packaging, and their perception of the healthiness associated with the colors. The taste appeal was rated on a scale from 1 (not tasty at all) to 7 (very tasty). The attractiveness of the packaging was rated from 1 (not attractive at all) to 7 (very attractive).

Results (see Table 1) indicate that participants did not perceive a significant difference in taste between red and green packaging (M_red = 4.81, SD_red = 1.45; M_green = 4.80, SD_green = 1.47; t(475) = 0.05, p = 0.96), thus excluding taste appeal as another possible explanation.

Table 1 Effect of packaging color on perceived food taste ratings.

Additionally, as shown in Table 2, there is no significant difference in the perceived attractiveness of the packaging between the red and green options (M_red = 4.16, SD_red = 1.50; M_green = 4.13, SD_green = 1.48; t(475) = 0.23, p = 0.82). Therefore, the potential explanation based on the attractiveness of the packaging is also ruled out.

Table 2 Effect of packaging color on perceived packaging attractiveness.

Caloric Estimation measurement

In this experiment, participants were asked to estimate the caloric content of the displayed foods, using the calorie content of walnuts as a reference. Specifically, participants were informed: “The calorie content of walnuts we commonly consume is 574 cal per 100 g. Please estimate the calorie content per 100 g for the food items shown in the picture above.”

Measurement of perceived healthiness

Perceived healthiness refers to consumers’ immediate judgment on the healthiness of a food item. This was measured using two items: perceived healthiness of the food (1 = very unhealthy, 7 = very healthy) and perceived increase in body fat after consuming the food (1 = very little, 7 = very much). The scores for perceived increase in body fat were reverse-scored and then averaged with the perceived healthiness score to construct a healthiness variable for the food (α = 0.787), where higher scores indicate greater perceived healthiness.

Experimental procedure

Study 1 employed a questionnaire method. Participants were instructed: “Hello: Thank you very much for your participation. We are currently conducting a study on food packaging. Please fill out the questionnaire on your phone or computer based on your actual situation, which will take about 5 minutes of your time. We solemnly promise that all data is anonymous and will only be used for this research.” Participants were first required to fill out personal information, then view product images presented in the questionnaire, estimate the calorie content of the products based on the reference calorie information provided, and answer questions about their perceived healthiness of the food. Subsequently, participants evaluated the taste of the food (1 = not tasty at all, 7 = very tasty), the attractiveness of the packaging (1 = not attractive at all, 7 = very attractive), and the healthiness perception related to the color (measured by the item “Color is related to people’s physical and mental health” (1 = strongly disagree, 7 = strongly agree)). To avoid practice and fatigue effects, the order of image presentation was balanced as “unhealthy-healthy-unhealthy.”

The study distributed 159 questionnaires, retrieved 159 effective responses, and then processed the data and performed statistical analysis.

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August 23, 2025
$3,000-luxury train in Japan canceled after crew caught drinking alcohol beyond allowable limit

“Some of the crew were repeatedly drinking more than they were allowed to as part of their routine quality control testing,” said a subsidiary of the East Japan Railway Company, commonly known as JR East.

The misdemeanor on the swanky Train Suite Shiki-shima started around September 2022, according to the subsidiary JR East View Tourism and Sales.

“This not only severely undermines trust in our business, but is unacceptable behavior for those in a position to oversee the itinerary of our guests,” it added.

Local media reports said that six staff members have so far been taken off duty, leaving the operator with what it called “manpower” shortages.

As a result, an upcoming jaunt due to begin on Aug. 30 around the bucolic regions of Niigata and Nagano has been canceled, it said on Aug. 21.

The journey of two nights and one day costs upwards of US$3,000 and promised, among other things, in-train dinner with French cuisine, expensive wines and a winery visit.

“We sincerely apologize for the inconvenience caused to those looking forward to (the trip),” JR East said.

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August 23, 2025
Multi-dimensional flux balance analysis to optimized resources and energy efficiency in MEC aided 5G networks

This section showcases the accomplishment of the suggested approach CBMDFBA and validates it using simulation data. Overall, energy usage and latency parameters concerning MDs and MHs are calculated. The simulation setup described in the section below is used to test the effectiveness of CBMDFBA.

Simulation setup

The geographical distribution of MDs is uniform inside the small dense area. Parameters used in simulation are shown in Table 4. BS is situated at a distance of 200 m from the area. 72 MDs are randomly located inside the small dense area of 20 m in length and 4.5 m in width. Out of 72 MDs, up to 20 available MHs can be selected randomly for computation offloading. For D2D connectivity, range for communication with MHs is 5 m. For both MDs and MHs, the maximum transmit power ({P_{hbox{max} }}) is 24 dBm. The network can tolerate a latency of 0.2 s. MDs and MHs have the following set of compute resources: ({f_{MD}})∈1 × 10⁹ CPU cycles/sec and ({f_{MH}})∈1 × 10⁹ CPU cycles/sec. For RES computation resource ({f_{RES}})∈15 × 10⁹ CPU cycles/sec and for ES is ({f_{ES}}) ∈40 × 10⁹ CPU cycles/sec. To compute 1-bit task,(Cr) ranges from 1500 to 2000. The devices effective system capacitance is ({C_Psi }) =10⁻²⁸. The channel noise and path loss exponent are ({N_0}) = −174 dBm and (alpha) = 4 respectively. The data size for each user with high computational demands is uniformly distributed in ({L_r}) ∈ [1 2.5] Mbits. MATLAB 2023a version was used to perform simulation outcomes. The system features Intel(R) Core (TM) i5-8250 CPU running at 1.6 GHz, 16 GB RAM, and 64-bit Windows 11.

Table 4 Simulation variables.

Simulation results

The results of various computing demands are discussed in this section. The performance is measured based on two parameters: latency and energy consumption. Total energy consumption is calculated by Eq. (16). Equations (1), (4), and (5). The difference in latency is vast between the proposed work and the existing work. So, latency is plotted on a logarithmic scale to differentiate the simulation results.

In Figs. 3 and 72 users have been considered when considering the ideal case of a dense area. And out of 72 users, five users are seeking task computation. A total of four schemes have been compared in Fig. 3 name as (1) Resource allocations using Q learning with considering parameter throughput- RA(QL-Munkres-TH), (2) Resource allocations using Q learning with considering parameter distance- RA(QL-Munkres-Dist), (3) Resource allocation with considering maximum power- RA(Max-Power), (4) Proposed scheme for resource allocation using CBMDFBA. The results have shown that the latency calculated in Fig. 3(a) for 1Mbps task size in the proposed scheme is reduced by 99.87% in comparison with RA(QL-Munkres-TH) scheme, 99.89% in comparison with RA(QL-Munkres-Dist) scheme and 99.73% in comparison with RA(Max-Power) scheme. The average latency has been calculated at 2.13ms only in the proposed scheme CBMDFBA. In Fig. 3(a), it is clear that the proposed algorithm is showing that the latency is reducing with increasing the number of users. In Fig. 3(b), the task size has been considered 1.5Mbps, and it found that 99.86% has reduced the latency, 99.88%, and 99.71%, respectively, to the scheme RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power). The average latency has been calculated at 3.75ms only in the proposed scheme CBMDFBA. Figure 3(b) shows that the proposed method decreases latency as the number of user increases. In addition, it is performing well, even with an increment in task size.

Fig. 3

Latency vs. MDs for (a) ({t_s}) = 1Mbps, (b) ({t_s}) = 1.5Mbps, (c) ({t_s}) = 2Mbps, (d) ({t_s}) = 2.5 Mbps.

Figure 3(c) shows that when compared to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power) with task size of 2Mbps resulted in a 99.87%, 99.89%, and 99.74% reduction in latency. According to the proposed CBMDFBA scheme, the average latency is 4.34 ms. It also indicates that the proposed algorithm’s latency is decreasing with increasing users. Figure 3(d) demonstrates that a task size of 2.5Mbps led to a 99.84%, 99.87%, and 99.68% reduction in latency when compared to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power). The average delay, as per the proposed CBMDFBA scheme, is 6.69ms. Also, the latency is decreasing with the number of users.

In Fig. 4, Energy consumption is calculated, and simulation results are compared. In Fig. 4(a), the average energy consumption is 973.4 J for the proposed CBMDFBA scheme, which is 53.56% less than a comparison of scheme RA(QL-Munkres-TH). And 61.20% less in comparison with scheme RA(QL-Munkres-Dist) and 67.67% less with scheme RA(Max-Power) for the task size of 1Mbps. Figure 4(b) demonstrates that a task size of 1.5Mbps led to a 72.82%, 75.62%, and 79.69% reduction in energy consumption when using CBMDFBA as compared to RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power).

Fig. 4

Energy usage vs. MDs for (a) ({t_s}) = 1Mbps, (b) ({t_s}) = 1.5Mbps, (c) ({t_s}) = 2Mbps, (d) ({t_s}) = 2.5 Mbps.

The average energy consumption is calculated at 899.1 J in the proposed scheme CBMDFBA. In Fig. 4(c), task size 2Mbps is considered, and it found that the energy consumption is reduced by 76.31%, 80.21%, and 83.51%, respectively, to the scheme RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power). The average energy consumption is 917.4 J only in the proposed scheme CBMDFBA. Figure 4(d) shows that, when the proposed scheme is compared to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power) with taking task size 2.5Mbps, it resulted in 83.26%, 86.01%, and 88.34% reduction in energy consumption. According to the proposed CBMDFBA scheme, the average energy consumption is 841 J. From Fig. 4, it is clear that energy consumption is increasing with the increasing number of users.

In next scenario, we have considered the 52 MDs and 20 MHz are available in dense areas. We have increased the number of MHs to see the variation in simulation results. In Fig. 5, latency has been calculated with varying numbers of MHs. Figure 5(a) shows that the CBMDFBA scheme lowers latency by 99.86% when compared to the RA(QL-Munkres-TH), 99.88% when compared to the RA(QL-Munkres-Dist) scheme, and 99.71% when compared to the RA(Max-Power) strategy for a 1Mbps task size.

Fig. 5

Latency vs. MHs for (a) ({t_s}) = 1Mbps, (b) ({t_s}) = 1.5Mbps, (c) ({t_s}) = 2Mbps, (d) ({t_s}) = 2.5 Mbps.

In the CBMDFBA scheme, the average latency is calculated at 2.27 ms. Figure 5(b) shows that, when comparing proposed scheme with scheme RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power), the latency is decreased by 99.84%, 99.87%, and 99.70%, respectively, with 1.5Mbps. In the proposed CBMDFBA system, the average latency is determined at 3.59ms. Task size of 2Mbps is examined in Fig. 5(c), and it is found that, in comparison to Schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power), the latency in the proposed scheme is decreased by 99.87%, 99.89%, and 99.72%, respectively. In the proposed CBMDFBA system, the average latency is 4.89 ms. Figure 5(d) shows that, when comparing scheme RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power) with proposed CBMDFBA, the latency is decreased by 99.88%, 99.90%, and 99.78%, respectively with task size 2.5Mbps. The proposed CBMDFBA technique yielded an average delay of 5.10 ms. From Fig. 5, it is evident that the latency is decreasing with the increase in the number of helpers, and it also shows better results for larger task sizes.

Fig. 6

Energy usage vs. MHs for (a) ({t_s}) = 1Mbps, (b) ({t_s}) = 1.5Mbps, (c) ({t_s}) = 2Mbps, (d) ({t_s}) = 2.5 Mbps.

Figure 6 presents the energy consumption calculation and a comparison of the simulation results. Figure 6(a) shows that the proposed CBMDFBA scheme’s average energy consumption is 955.9 J, 53.91% less than scheme RA(QL-Munkres-TH). Additionally, there was a 60.82% decrease from scheme RA(QL-Munkres-Dist) and a 67.35% decrease from scheme RA(Max-Power). In Fig. 6(a), the task size is considered 1Mbps.

Compared to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power), Fig. 6(b) shows that a task size of 1.5Mbps resulted in a reduction of 68.93%, 74.05%, and 78.37% in energy usage for the proposed scheme. The proposed approach calculates the average energy usage at 943.7 J. When comparing the proposed scheme CBMDFBA to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power), Fig. 6(c) shows that a task size of 2Mbps resulted in a reduction in energy consumption of 78.29%, 81.87%, and 84.89% with schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power) respectively.

Fig. 7

Latency vs. RES computation (a) ({t_s}) = 1Mbps, (b) ({t_s}) = 1.5Mbps, (c) ({t_s}) = 2Mbps, (d) ({t_s}) = 2.5 Mbps.

The total average energy consumption in the proposed scheme is 908.3 Joules. Comparing the CBMDFBA to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power) with a task size of 2.5Mbps, Fig. 6(d) shows that the reduction in energy usage is reduced by 79.45%, 82.83%, and 85.69% respectively for schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power) with proposed scheme. The average energy usage is 1036 J for the CBMDFBA scheme. In Fig. 6, it is clearly shown that the energy consumption is increasing with the increasing number of helpers due to the increment of the interference between the devices.

Figure 7 presents simulation results for latency vs. RES computation (cycle/sec). Figure 7(a) shows that the proposed CBMDFBA scheme’s average latency is 2.09ms, 99.88% less than scheme RA(QL-Munkres-TH). Additionally, there is a 99.90% reduction from scheme RA(QL-Munkres-Dist) and a 99.76% reduction from scheme RA(Max-Power). In Fig. 7(a), the task size is considered to be 1Mbps. Figure 7(b) shows that, when comparing the proposed scheme with scheme RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power), the latency is decreased by 99.88%, 99.90%, and 99.75%, respectively with considering task size 1.5 Mbps. In the proposed CBMDFBA scheme, the average latency is determined to be 3.05ms. The task size of 2Mbps is examined in Fig. 7(c), and it is found that, in comparison to Schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power), the latency in the proposed scheme is decreased by 99.86%, 99.88%, and 99.71%, respectively. The average latency in the proposed CBMDFBA system is calculated at 4.61 ms. Figure 7(d) shows that, when comparing scheme RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power) with CBMDFBA, the latency is decreased by 99.86%, 99.88%, and 99.72%, respectively, when the task size selected 2.5 Mbps. The proposed CBMDFBA technique yielded an average delay of 5.93ms. Figure 7 shows that the proposed scheme performs well even if the task size increases. Latency is decreasing; even RES computation is expanding.

Figure 8 presents the energy consumption calculation and a comparison of the simulation results for RES computation. Figure 8(a) shows that the proposed CBMDFBA scheme’s average energy consumption is 1114 J, 46.52% less than scheme RA(QL-Munkres-TH). Additionally, there is a 55.31% reduction from scheme RA(QL-Munkres-Dist) and a 62.76% reduction from scheme RA(Max-Power). In Fig. 8(a), the size of the task is considered 1Mbps. Compared to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power), Fig. 8(b) shows that a task size of 1.5Mbps resulted in a reduction of 66.36%, 71.89%, and 76.58% in energy usage for the proposed scheme.

Fig. 8

Energy usage vs. RES computation for (a) ({t_s}) = 1Mbps, (b) ({t_s}) = 1.5Mbps, (c) ({t_s}) = 2Mbps, (d) ({t_s}) = 2.5 Mbps.

The proposed approach determines the average energy usage as 989.4 J. When comparing the proposed scheme CBMDFBA to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power), Fig. 8(c) shows that a task size of 2Mbps resulted in a reduction in energy consumption of 76.65%, 80.49%, and 83.74%. The total average energy consumption in the proposed scheme is 937.7 Joules. Comparing the CBMDFBA to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power) with a task size of 2.5Mbps, Fig. 8(d) shows that the reduction in energy usage is 81.63%, 84.66%, and 87.21%. The average energy usage is 933.4 J per the planned CBMDFBA system. In Fig. 8, it is clearly shown that the energy consumption increases with the increase in the RES computation due to the increase in the interference between the devices.

Fig. 9

latency vs. ES usage for (a) ({t_s}) = 1Mbps, (b) ({t_s}) = 1.5Mbps, (c) ({t_s}) = 2Mbps, (d) ({t_s}) = 2.5 Mbps.

Figure 9 presents simulation results for latency vs. ES computation (cycle/sec). Figure 9(a) shows that the proposed CBMDFBA scheme’s average latency is 2.47 ms, 99.86% less than scheme RA(QL-Munkres-TH). There are 99.88% and 99.71% reductions, respectively, to scheme RA(QL-Munkres-Dist) and RA(Max-Power). In Fig. 9(a), the size of the task is considered to be 1Mbps. Figure 9(b) shows that, when comparing the proposed scheme with scheme RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power), the latency is decreased by 99.87%, 99.89%, and 99.72%, respectively with task size 1.5 Mbps. In the proposed CBMDFBA scheme, the average latency is calculated at 3.53ms. The task size of 2Mbps is examined in Fig. 9(c), and it is found that, in comparison to Schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power), latency in the proposed scheme is decreased by 99.86%, 99.89%, and 99.72%, respectively. In the proposed CBMDFBA scheme, the average latency is determined at 4.73 ms. Figure 9(d) shows that, when comparing scheme RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power) with CBMDFBA, the latency is decreased by 99.88%, 99.90%, and 99.75%, respectively with task size 2.5 Mbps. The proposed CBMDFBA technique yielded an average delay of 4.94ms. Figure 9 shows that the proposed scheme performs well even if task size increases. Latency also decreases even with ES computations increasing.

Fig. 10

Energy consumption vs. ES computation for (a) ({t_s}) = 1Mbps, (b) ({t_s}) = 1.5Mbps, (c) ({t_s}) = 2Mbps, (d) ({t_s}) = 2.5 Mbps.

Figure 10 presents the energy consumption calculation and a comparison of the simulation results for ES computation. Figure 10(a) shows that the proposed CBMDFBA scheme’s average energy consumption is 974.4 J, which is 53.33% less than scheme RA(QL-Munkres-TH), 61.01% less than scheme RA(QL-Munkres-Dist) and a 67.51% less from scheme RA(Max-Power) for 1Mbps task size. Compared to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power), Fig. 10(b) shows that a task size of 1.5Mbps resulted in a reduction of 68.54%, 73.71%, and 78.09% in energy usage for the proposed scheme. The proposed approach determines the average energy usage as 964.8 J. When comparing the proposed scheme CBMDFBA to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist) and RA(Max-Power), Fig. 10(c) shows that a task size of 2Mbps resulted in a reduction in energy consumption of 75.96%, 79.92%, and 83.26%. The total average energy consumption in the proposed scheme is 982.4 Joules. Comparing the CBMDFBA to schemes RA(QL-Munkres-TH), RA(QL-Munkres-Dist), and RA(Max-Power) with a task size of 2.5Mbps, Fig. 10(d) shows that the reduction in energy usage is 78.44%, 81.99%, and 84.99%. The average energy usage is 1037 J, as per the CBMDFBA. In Fig. 10, it is clearly shown that the energy consumption increases with enlarge in the RES computation due to surge in the interference between the devices.

Fig. 11

Fairness Index with varying (a) Mobile users, (b) mobile helps, (c)({f_{RES}}), (d) ({f_{ES}}).

Fairness index is calculated with the help of:

$$f(x)=frac{{(sumlimits_{{i=1}}^{n} {{x_i}{)^2}} }}{{nsumlimits_{{i=1}}^{n} {x_{i}^{2}} }}$$

(29)

A high fairness index means resources are distributed efficiently in the system. A comparison between all the baseline algorithms and the proposed algorithm is shown in Fig. 11. The figure shows that the proposed algorithm has the highest fairness index.

Figure 12 represents a plot between energy efficiency and edge server computation for the all baseline algorithms and proposed algorithm for varying MUs, MHs, ({f_{RES}})and({f_{ES}}). The figure shows that the energy efficiency is highest for the proposed algorithm compared to baseline algorithms.

Fig. 12

Energy Efficiency with varying (a) Mobile users, (b) mobile helps, (c)({f_{RES}}), (d) ({f_{ES}}).

Convergence of the proposed algorithm CBMDFBA is shown in Fig. 13. Average Q-values settle after a certain number of repetitions.

Fig. 13

Convergence behaviour of CBMDFBA.

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August 23, 2025
Knowledge, attitudes, and practices regarding home-based cardiac rehabilitation in patients with chronic heart failure
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This section outlines the deception detection methodology proposed in this study. It discusses the traditional SQM metrics, as well as the MuSD and MuSDA metrics and their threshold calculation methods. Additionally, the computation process of the WMA-BC algorithm is also examined.

Spoofing detection process

The spoofing detection process (Fig. 2) follows a sequential workflow: First, the GNSS receiver demodulates the intermediate frequency (IF) signal. Then, multiple correlators process this signal to generate correlator outputs, which are used to calculate two key metrics—MuSDA and MuSD. These metrics undergo further processing through the WMA-BC algorithm for enhanced detection capability. Finally, the processed metric values (M_{x}) are compared against thresholds (theta_{x}) for spoofing signals to determine whether the received signal is authentic or spoofed.

Fig. 2

Flowchart of WMA-BC for GNSS spoofing detection.

Expressions of the monitoring metrics

Monitoring metrics utilize the correlator output parameter with different composition methods to detect spoofing signals. To understand the metrics, the statistical characteristics must be known. The mean value and noise variance of the metrics can be obtained through calculations, and differences in the signal-to-noise ratio, correlation integral time, and correlator positions can change the noise variance of the metrics. We considered six SQM metrics for comparison: the ELP, ratio, delta, double delta, slope, and double slope metrics. The detailed derivation of the noise variance of each metric is presented in the Appendix.

Table 1 summarizes the definitions and statistical characteristics of the SQM metrics. ({{I_{E} } mathord{left/ {vphantom {{I_{E} } {Q_{E} }}} right. kern-0pt} {Q_{E} }}) and ({{I_{L} } mathord{left/ {vphantom {{I_{L} } {Q_{L} }}} right. kern-0pt} {Q_{L} }}) are the values of the early/late correlator in the in-phase/quadrature correlators, where (E) and (L) are 0.5 and -0.5, respectively. (I_{0}) denotes the output value of the maximum correlator; (I_{{d_{1} }}), (I_{{d_{2} }}), (I_{{ – d_{1} }}) and (I_{{ – d_{2} }}) are the output values of the additional correlators, where the negative sign represents early and no negative sign represents late, (d) denotes the spacing between the correlators and the maximum correlator, and the numbers are used as identifiers. The unit of (d) is chips.

Table 1 Definitions and theoretical statistics of the SQM monitoring metrics.

MuSD and MuSDA metrics

This section describes the NeSD, MiSD, FaSD, MuSD, and MuSDA metrics. Correlators at different locations have distinct offset detection advantages. NeSD, MiSD, and FaSD have complementary properties because the correlators used are at specific locations. However, relying solely on the correlators used by NeSD, MiSD, or FaSD to obtain spoofing detection results is unreliable. MuSD and MuSDA effectively utilize all the different correlators used by NeSD, MiSD, and FaSD by aggregating slope information from correlators at different offsets. This method leverages this diversity to build a more comprehensive signal integrity profile, efficiently increasing the spoofing detection range and preventing, slope, ratio, and ELP from effectively detecting only significant changes at the top or both sides of the correlation peak.

The correlators needed to construct the metrics are shown in Fig. 3. The MiSD correlator (d_{2} = 0.5) chips, which is the (E – L) correlator of the receiver, and (d_{0} = 0) chips, which is the prompt correlator of the receiver. The NeSD and MiSD correlators are located on either side of the (E – L) correlator. The correlator spacing is (d_{1} > d_{2} > d_{3} > d_{0}) , which is determined based on the offset detection advantages of using correlators at different locations.

The (d_{3}) correlator of NeSD is effective for monitoring the ACF near-point distortion by very small code phase difference spoofing and low power spoofing due to its proximity to the prompt correlator. The NeSD can be expressed as

$$M_{NeSD} = frac{{I_{{ – d_{3} }} – I_{0} – left( {I_{0} – I_{{d_{3} }} } right)}}{{I_{0} }}$$

(10)

Intermediate code phase difference spoofing causes ACF distortion near the correlator, reducing the spoofing detection capability of NeSD for middle and far distortion points. MiSD utilizes the receiver’s original (E – L) correlator to supplement the NeSD performance. The metric is defined as

$$M_{MiSD} = frac{{I_{{ – d_{2} }} – I_{0} – left( {I_{0} – I_{{d_{2} }} } right)}}{{I_{0} }}$$

(11)

Due to correlation limitations, NeSD and MiSD have difficulty detecting small ACF distortions at far points. Thus, to prevent spoofing leakage detection, the far point correlator (d_{1}) is deployed beyond the (E – L) correlator, and the FaSD metric is defined as follows:

$$M_{FaSD} = frac{{I_{{ – d_{1} }} – I_{0} – left( {I_{0} – I_{{d_{1} }} } right)}}{{I_{0} }}$$

(12)

MuSD is a joint decision metric that is not directly obtained by the correlators but is jointly determined by the NeSD, MiSD, and FaSD results through logical association operations. The MuSD metric is expressed as follows:

$$H_{MuSD} { = }left{ {begin{array}{*{20}c} {H_{1} , , H_{NeSD} cup H_{MiSD} cup H_{FaSD} } \ {H_{0} ,{text{ others }}} \ end{array} } right.$$

(13)

where (H_{SDN}), (H_{SDI}), and (H_{SDF}) are the NeSD, MiSD, and FaSD decision results, respectively.

The MuSDA metric is derived from the receiver’s E, L, and P correlators, as well as additional correlators, using the mean-value difference method, and the MuSDA metric is defined as

$$M_{MuSDA} = sumlimits_{i = 1}^{3} {left| {frac{{I_{{ – d_{i} }} – I_{0} – left( {I_{0} – I_{{d_{i} }} } right)}}{{3I_{0} }}} right|}$$

(14)

MuSD and MuSDA use the same correlator and can therefore be used simultaneously to detect spoofing.

Theoretical thresholds and decision rules for metrics

The threshold for the metrics can be adaptively calculated based on the desired false alarm rate and the statistical characteristics. For satellite navigation signals, the hypothesis testing theory of signal processing is used to identify spoofing signals, with a null hypothesis (H_{0}) indicating that no spoofing signal exists and an alternative hypothesis (H_{1}) indicating that a spoofing signal exists. Assuming that the probability density function of the noise in the case of (H_{0}) follows a normal distribution with mean (mu_{x}) and standard deviation (delta_{x}), the false alarm rate (P_{fa}) is expressed as

$$P_{fa} = rho (left| {M_{x} } right| > left. {theta_{x} } right|H_{0} ) = int_{{theta_{x} }}^{infty } {frac{1}{{sqrt {2pi } delta_{x} }}e^{{ – frac{{(x – mu_{x} )^{2} }}{{2delta_{x}^{2} }}}} dx}$$

(15)

Assuming that (t = {{left( {x – mu_{x} } right)} mathord{left/ {vphantom {{left( {x – mu_{x} } right)} delta }} right. kern-0pt} delta } = {{left( {theta_{x} – mu_{x} } right)} mathord{left/ {vphantom {{left( {theta_{x} – mu_{x} } right)} delta }} right. kern-0pt} delta })

$$begin{gathered} P_{fa} = rho (left| {M_{x} } right| > left. {theta_{x} } right|H_{0} ) = int_{{frac{{theta_{x} – mu_{x} }}{{delta_{x} }}}}^{infty } {frac{1}{{sqrt {2pi } }}e^{{ – frac{{t^{2} }}{2}}} dt} hfill \ { = }qleft( {frac{{theta_{x} – mu_{x} }}{{delta_{x} }}} right) = frac{1}{2}erfcleft( {frac{{theta_{x} – mu_{x} }}{{sqrt 2 delta_{x} }}} right) hfill \ end{gathered}$$

(16)

where (q(x) = int_{x}^{infty } {{1 mathord{left/ {vphantom {1 {left( {2pi } right)^{{{1 mathord{left/ {vphantom {1 2}} right. kern-0pt} 2}}} exp left[ {{{ – t^{2} } mathord{left/ {vphantom {{ – t^{2} } 2}} right. kern-0pt} 2}} right]dt}}} right. kern-0pt} {left( {2pi } right)^{{{1 mathord{left/ {vphantom {1 2}} right. kern-0pt} 2}}} exp left[ {{{ – t^{2} } mathord{left/ {vphantom {{ – t^{2} } 2}} right. kern-0pt} 2}} right]dt}}}) is the complementary cumulative distribution function of the standard normal distribution and (erfc(x) = {2 mathord{left/ {vphantom {2 {pi^{{{1 mathord{left/ {vphantom {1 2}} right. kern-0pt} 2}}} }}} right. kern-0pt} {pi^{{{1 mathord{left/ {vphantom {1 2}} right. kern-0pt} 2}}} }}int_{x}^{infty } {exp left[ { – t^{2} } right]} dt) is the complementary error function. For all of the metrics, the threshold (theta_{x}) can be expressed as

$$theta_{x} = sqrt 2 sigma_{x} erfc^{ – 1} (2P_{fa} ) + mu_{x}$$

(17)

where (erfc^{ – 1} (x)) is the inverse function of (erfc).

The false alarm rate can be flexibly adjusted according to the specific requirements of different application scenarios. For instance, high-risk scenarios may tolerate a slightly higher false alarm rate to ensure critical events are not missed, whereas low-risk applications require stricter control over the false alarm rate to avoid unnecessary disruptions.

Similarly, the detection rate can be expressed as

$$P_{d} = rho (left| {M_{x} } right| > left. {theta_{x} } right|H_{1} )$$

(18)

In the spoofing monitoring process, the decision is divided based on the results of the comparison between the metric measurement and its threshold. The discriminant is as follows:

$$H_{decition} { = }left{ {begin{array}{*{20}c} {H_{1} {, }left| {M_{x} } right| > left| {theta_{x} } right|} \ {H_{0} {text{, others }}} \ end{array} } right.$$

(19)

If the metric measurements exceed the thresholds, there is a spoofing signal; otherwise, there is no spoofing signal.

Weighted moving average bias correction

Noise, spoofing signals and other interference sources all cause transient or short-term fluctuations in metric data. When the spoofed signal operates in the frequency unlocking mode, the relative carrier phases of the real and spoofed signals change over time, leading to significant oscillations in the monitoring metrics and causing unnecessary false alarms³³. To reduce the influence of noise interference, we propose the weighted moving average bias correction algorithm, which can be applied to metric data. This approach considers recent data obtained over time, smooths the curve of the monitoring data, reduces the influence of random interference, and improves the robustness and detection performance of the metrics. This subsection describes the computational process and analyzes the simulation results obtained with this method. The traditional weighted moving average algorithm (WMA) expression is

$$P_{t} = beta P_{t – 1} + (1 – beta )M_{t}$$

(20)

where (P_{t}) and (P_{t – 1}) are the predicted values of the monitoring data at moments (t) and (t – 1) , respectively.(M_{t}) is the measured value at moment (t), where (beta) represents the rate of the decay weights, and its expression is

$$beta = 1 – frac{1}{{T_{c} }}$$

(21)

The moving window size in the WMA-BC algorithm is directly related to the receiver’s PIT, as (T_{c}) represents the minimum time interval over which coherent signal accumulation occurs. Therefore, we set the window size equal to the PIT.

During the receiver’s operation, we adopt an adaptive PIT adjustment strategy based on the scene type to optimize system performance. This mechanism determines the current scene type (low-speed/static or dynamic) by analyzing the Doppler rate (Delta {text{f}}) of change and dynamically adjusts the PIT. When the Doppler rate of change is less than or equal to 2 Hz/s, the system identifies the scene as low-speed/static, and the PIT is set to 10 ms to save computational resources and improve response speed. When the Doppler rate of change exceeds 2 Hz/s, the system identifies the scene as dynamic, and the PIT is adjusted to 100 ms to accommodate environments with large frequency fluctuations. The PIT can be expressed as:

$$T_{c} = left{ {begin{array}{*{20}c} {10 , ms, , Delta {text{f}} le {text{2 Hz/s}}} \ {100 , ms, , Delta {text{f > 2 Hz/s }}} \ end{array} } right.$$

(22)

According to (20), we obtain the following expression:

$$P_{t} = (1 – beta )left[ {M_{t} + beta M_{t – 1} + beta^{2} M_{t – 2} + beta^{3} M_{t – 3} ldots + beta^{t – 1} M_{1} } right]$$

(23)

The WMA algorithm smooths ACF data by averaging past observations, giving more weight to recent data. While this reduces jitter, it can introduce bias due to small initial values. To address this, we propose the WMA-BC algorithm, which adds a bias correction step to reduce the discrepancy between smoothed and actual values, improving prediction accuracy. The WMA-BC algorithm is as follows:

$$P_{{biased_{t} }} = frac{{P_{t} }}{{1 – beta^{t} }}$$

(24)

where (P_{{biased_{t} }}) is the weighted moving average bias correction, (P_{t}) is the predicted weighted moving average.

Experimental results and discussion

Performance of the WMA-BC algorithm

To evaluate the performance of the WMA-BC algorithm, we conducted experiments on the TEXBAT dataset. In the TEXBAT dataset, Cases 2–8 are examples of synchronized spoofing intrusions, while Case 1 is an example of spoofing switching³⁴.

In Case 2, the spoofed signal has a higher power (+ 10 dB) than does the authentic signal, and the spoofers operate in frequency-unlocked mode (the carrier phase difference between the spoofed and authentic signals is not fixed). Case 3 differs from Case 2 in that the spoofed signal operates in frequency-locked mode (the carrier phase difference between the spoofed and authentic signals is fixed), and the power is reduced from 10 dB to 1.3 dB.

We compared the spoofing detection rates of SQM metrics using WMA-BC, WMA, MA-based, and MV-based algorithms, as well as MuSDA and MuSD metrics in Case 2 (Fig. 4(a)) and Case 3 (Fig. 4(b)). The spoofing detection times ranging from 60 to 300 s and the predetection integration time (T_{c} = 100ms), and (P_{fa} le 10^{ – 7}). The detection rate is defined as

$${text{detection rate}} = frac{{text{Samples that exceed the detction threshold}}}{{text{Samples in which deception exists}}}$$

(25)

In Case 2, the detection rates of the metrics obtained based on the WMA-BC algorithm are all improved, but the effect differs for different metrics, with the detection rates of the slope, ratio, MuSDA and MuSD metrics significantly improved by more than 70%. As the detection rates of the double slope, delta, double delta, and ELP metrics were originally close to 0, the improvement in the detection rate was limited. Case 3 shows results similar to those of Case 2; the metrics obtained based on the WMA-BC algorithm have higher detection rates, and the detection rates of the metrics improve by approximately 22% to 53%.

Experimental data analysis shows significant performance differences among the four methods in the spoofing detection task. In Case 2 testing, the WMA-BC method performed the best, achieving detection rates of 100% and 81.4% for the MuSDA and slope metrics, respectively, which represents an improvement of 4.8% and 38.3% compared to the WMA algorithm. In comparison, the MA method only reached 66.3% and 26.2%, while the MV method achieved 40.4% and 32.5%. Notably, the MV method completely failed on the ratio metric (0% detection rate), whereas WMA-BC maintained an effective detection rate of 87.1%, which is an improvement of 15.1% compared to WMA.

Further analysis of the Case 3 data reveals that the advantage of WMA-BC is even more pronounced on the slope metric, where its detection rate was more than 30% higher than both the MA and MV methods, with an improvement of about 5% to 20% compared to the WMA method. This method also maintained stable performance on the double slope, delta, MuSDA, and MuSD metrics, demonstrating strong overall performance. In contrast, while the MA method performed reasonably well on the ratio and MuSD metrics, it achieved only a 14.1% detection rate on the delta metric, showing clear performance limitations. The MV method exhibited unbalanced characteristics: it performed excellently on the double slope (63.7%), double delta (63.7%), and ELP (52.6%) metrics but underperformed on key metrics such as ratio (26.2%), MuSDA (5.9%), and MuSD (23.4%).

Overall, WMA-BC demonstrated clear advantages over WMA, MV and MA in terms of performance. The superior performance of WMA-BC is primarily attributed to its weighted computation mechanism, which dynamically adjusts weights over time, effectively enhancing feature differentiation. In contrast, the MA method, due to its simple mean calculation, is prone to losing crucial temporal information. The MV method, which treats all data points within the window equally, cannot implement variance calculations that incorporate features such as exponential decay weights, which are more suited to time-series characteristics, resulting in insufficient performance.

Quantitative analysis demonstrates that WMA-BC significantly enhances the discriminative capability of embedded GNSS systems, achieving more than a 70% improvement in detection rate for key signal metrics. For instance, in Case 2, the Slope metric shows a remarkable increase from 3.6% (raw metric) to 81.4% with WMA-BC, outperforming the MA approach at 26.2% and the MV method at 32.5%.

Despite the computational burden associated with multi-correlator architectures, such as MuSDA/MuSD, which require around 750 M floating-point operations per second (FLOPs), including an overhead of 200 M FLOPs due to additional correlators—WMA-BC introduces only a minimal overhead of 0.50 M FLOPs (just 0.07% of the baseline), along with an additional 48 kB of RAM usage (Table 2).

Table 2 FLOPs and RAM overheads of three algorithms under multi-correlator metrics.

This efficiency makes WMA-BC, along with MuSD and MuSDA metrics, highly suitable for deployment on resource-constrained embedded platforms. For example, when implemented on the TMS320C6748 processor (clocked at 456 MHz with a peak performance of 3648 MFLOPs and a typical power consumption of 1.1W), the added computational load is relatively small, representing less than 5.5% of the total processing capacity. Moreover, WMA-BC maintains linear time complexity O(n), ensuring robust scalability for real-time applications—unlike MV, which has O(n²) complexity and incurs a 13 M FLOP overhead, approximately 72 times greater than that of WMA-BC.

These findings underscore WMA-BC’s unique ability to balance robust spoofing detection with stringent resource efficiency, fulfilling the demanding requirements of real-time GNSS spoofing detection systems in resource-constrained environments.

We calculated and plotted the receiver operating characteristic curves for Case 2 (Fig. 5(a)) and Case 3 (Fig. 5(b)), and performed statistical analysis (Table 3). In the experiments, (P_{d}) and (P_{fa}) were measured by continuously decreasing the metric thresholds. We evaluated the AUC, which is an important parameter for detection performance.

Table 3 The summary of AUC of ROC curves for different metrics.

In Case 2, the AUC values of the metrics obtained based on the WMA-BC algorithm are markedly larger than those of the metrics obtained without the WMA-BC algorithm and those using the WMA algorithm. The AUC area with the WMA-BC algorithm increased by 0.01 to 0.197 compared to the WMA algorithm, and increased by 0.043 to 0.376 compared to the original metrics. Additionally, the MuSDA metric obtained based on the WMA-BC algorithm has an AUC equal to 1, demonstrating a 100% detection rate with no false alarms. In Case 3, the AUC area of the metrics combined with the WMA-BC algorithm increased by 0.01 to 0.072 compared to the WMA algorithm, and the AUC increased by 0.038 to 0.207 compared to the original metrics, which also indicates that these metrics achieved stronger detection capabilities.

In summary, the WMA-BC algorithm-based metrics achieve enhanced spoofing detection rates and superior performance with minimal computational overhead. The GNSS receiver thereby attains improved ROC performance—regardless of whether spoofing signals operate in frequency-locked or frequency-unlock modes, and irrespective of spoofing signal power being higher than or approximately equal to authentic signals.

Spoofing detection experiments with different code phase offsets and carrier phase offsets

To examine the detection performance of various metrics in synchronized spoofing against different code phase offsets and carrier phase offsets (based on the WMA-BC algorithm), we perform experiments by simulating a GPS satellite with the following signal simulation parameters: ({C mathord{left/ {vphantom {C {N_{0} }}} right. kern-0pt} {N_{0} }}) is 45 dB, the C/A code phase difference (mathop tau limits^{ sim } = left| {tau_{s} – tau_{a} } right|) between the authentic signal and the spoofing signal ranges from 0 to 1 chip, with a step size of 0.005 chips, and carrier phase difference (mathop {theta_{s} }limits^{ sim } = left| {theta_{s} – theta_{a} } right|) ranges from 0 to 2π, with a step size of 0.1π, for a total of 4221 grid experiments. Due to the high similarity between spoofing signals and authentic signals in the experiment, and considering the tracking stability of the receiver and the timeliness of spoofing detection, (T_{c}) is 10 ms. The correlators used to obtain the MuSD and MuSDA metrics in the experiments are (d_{1} = 0.9) chips, (d_{2} = 0.5) chips, and (d_{3} = 0.1) chips.

The spoofing detection rates at the experimental grid points are demonstrated in Fig. 6, where the grid color indicates the spoofing detection probability. Each grid represents the detection rate in one experiment, and (P_{fa} le 10^{ – 7}), which can effectively reflect the detection sensitivity of the metrics obtained in each experiment. The detection rates of some metrics decrease in cases with long intrusion times, such as the slope, double slope, delta, and double delta metrics. This is because in the early stage of the spoofing attack, the output values of the early and late correlators change or differ significantly, and the detection difficulty is small. However, in the spoofing attack of the middle or late stages, the change in the output values of the early and late correlators decreases, and the detection difficulty increases. However, the MuSD and MuSDA metrics are obtained using multiple correlators, which can monitor small fluctuations in bilateral slopes at multiple points simultaneously, ensuring high sensitivity and detection rates.

To evaluate the detection performance of the metric more objectively, we evaluated the detection coverage of each metric. The detection coverage is the ratio of the detectable area to the total area in a certain detection region. This value is a more comprehensive reflection of the performance of the metrics. The result of each experiment is 1 unit, and the total number of units is 4221. The detection coverage is defined as

$${text{detection coverage}} = frac{{text{Detectable area }}}{{text{Total area}}}$$

(26)

The detectable area in (26) is the sum of the detectable grid points, and we set a minimum acceptable detection rate of (P_{{d_{min } }}). If (P_{d} le P_{{d_{min } }}), the grid is undetectable, and its grid value is recorded as 0; otherwise, the grid value is set as 1.

Figure 7 shows the detection coverage of each metric when the minimum acceptable detection rate is set to 0.8. The yellow region in the figure represents the detectable region ((P_{d} ge 80%)), and the blue region represents the undetectable region. For both the slope and delta metrics with two correlators and the double slope and double delta metrics with four correlators, the detectable area is smaller than that of the other metrics, and the detection coverage is less than 60%. For the ELP and ratio metrics, undetectable grids are found at their edges or at the center in more places. In contrast, the MuSD and MuSDA metrics have mainly detectable areas, except for the undetectable areas at the edges of (mathop tau limits^{ sim } le 0.055) and (left{ {begin{array}{*{20}c} { , 0 le mathop {theta_{s} }limits^{ sim } le 0.6pi } \ {1.4pi le mathop {theta_{s} }limits^{ sim } le 2pi } \ end{array} } right.). The existence of this blind spot arises from the fact that when the code/carrier phase shift of the deception signal is extremely small, its impact on the correlation peak of the real signal is negligible, typically manifesting as a very weak “boost” or “distortion.”

Under the stable operation of the receiver, the receiver experiences fluctuations such as thermal noise and quantization noise, which are very similar to the changes caused by spoofing signals. The adaptive threshold (theta_{x}) we set has a statistical fluctuation offset range given by

$$offset = sqrt 2 sigma_{x} erfc^{ – 1} (2P_{fa} )$$

(27)

When the spoofing signal is extremely similar to the true signal, the metric shift (Delta x) caused by the spoofing signal is very small, and the subtle changes induced by the spoofing signal are easily masked by the inherent noise. The expression is:

$$Delta x = left| {M_{spoofing} – mu_{x} } right|$$

(28)

where (M_{spoofing}) is the measured metric’ value when spoofing is present. Its shift mainly comes from the minor distortions of the signal generator and the additional noise introduced by the spoofing signal itself. When the metric shift (Delta x) caused by the spoofing signal is less than or equal to the statistical fluctuation range (offset) , the receiver cannot effectively detect the spoofing, leading to a detection blind spot.

The detection coverage of the eight detection metrics is summarized (Fig. 8), and the performance of the metrics can be ranked as follows: delta (26.4%) < slope (37.4%) < double delta (52.4%) < double slope (58.3%) < ELP (61.1%) < ratio (73.3%) < MuSDA (95.8%) < MuSD (96.1%). MuSD has the highest detection coverage of 96.1%, and MuSDA has a slightly lower detection coverage than the MuSD metric, with a value of 95.8%, which is approximately 22% to 69% higher than that of the other metrics. These results show that MuSDA and MuSD possess smaller blind zones and outperform the other metrics in terms of code phase offset and carrier phase offset detection.

We evaluated the performance of MuSD under different correlator spacing combinations (Table 4). The experimental results show that as (d_{1}) decreases and (d_{3}) increases (with the receiver’s inherent correlator spacing (d_{2} = 0.5)), the detection coverage of MuSD decreases significantly. In this experiment, the configuration (d_{1} = 0.9), (d_{2} = 0.5), and (d_{3} = 0.1) achieved the highest detection coverage (95.8%). This result indicates that this configuration effectively ensures high detection coverage of MuSD across different code phase offset and carrier offset experiments, demonstrating the strongest robustness.

Table 4 The detection coverage of the MuSD metric under different combinations of correlator spacings.

Test with the TEXBAT dataset

To further validate the performance of the metrics (based on the WMA-BC algorithm), we used seven spoofing intrusion cases from the TEXBAT dataset as tests. The battery can be considered the data component of an evolving standard meant to define the notion of spoof resistance for civil GPS receivers. According to this standard, successful detection of or imperviousness to all spoofing attacks in TEXBAT, or a future version thereof, could be considered sufficient to certify a civil GPS receiver as spoof resistant³⁴. It includes dynamic, static, power matching, carrier/code phase matching, and other scenarios (Table 5), among which the challenge of spoofing detection on a dynamic platform is to distinguish spoofing effects from natural fading and multipath.

Table 5 Summary of the TEXBAT dataset.

We detected the signals from 60 to 300 s for each case (240 s in total) and selected the period from 120 to 300 s (spoofing intrusion phase) to calculate the spoofing detection rate. The PIT was set to (T_{c} = 100ms), and the false alarm rate (P_{fa} le 10^{ – 7}).

Through experiments based on the TEXBAT dataset, we visualized the detection rate for each metric (Fig. 9) and performed statistical analysis (Table 6). This result reflects the detection effectiveness in defending against deceptive intrusions. Case 2 is a time-specific attack. The detection rates of the slope, ratio, MuSDA, and MuSD metrics are relatively high, reaching greater than 80%, with MuSDA and MuSD reaching 100%. In contrast, the detection rates of the double slope, delta, double delta, and ELP metrics are not more than 25%. Case 3 is the same as Case 2 except that the power difference between the spoofed and authentic signals is reduced from 10 dB to 1.3 dB, and the spoofers operate in frequency-locked mode. The frequency-locked mode increases the change in the correlator detection value, which is favorable for spoofing detection. The detection rates of the double slope, delta, double delta, and ELP metrics are improved in this case, and the ratio, MuSDA, and MuSD metrics maintain high detection rates of 81.9%, 85.2%, and 94.4%, respectively. Case 4 is the same as Case 3 except that the power difference between the spoofed and authentic signals is reduced (from 1.3 dB to 0.4 dB), and the spoofed signals are position offset-type spoofs. Compared to the results in Case 3, the detection rates of the metrics decrease, while the MuSDA and MuSD metrics still maintain high detection rates of 92.9% and 99.1%, respectively. Case 5 is similar to Case 2, except that the receiver platform is changed from static to dynamic, and obvious changes in the power and phase values occur, making spoofing detection more difficult. The detection rates of the double slope, delta, and double delta metrics are close to 0 in this case. The detection rates of the slope and ratio metrics decrease to 10.3% and 48.7%, respectively, while the MuSDA and MuSD metrics maintain high detection rates of 97.6% and 99.9%, respectively. Case 6 is similar to Case 4, except that the receiver platform is changed from static to dynamic. In Case 6, the detection rates of the various metrics show different degrees of change, with the slope, double slope, delta, double delta, ELP, ratio, MuSDA, and MuSD metrics obtaining detection rates of 20%, 55.3%, 22.5%, 53.6%, 4.9%, 63.7%, 76.1%, and 98.8%, respectively. Case 7 is similar to Case 3, except that a carrier phase alignment strategy is implemented for the spoofed signals. In this case, the delta metric has a detection rate of 0%, the ELP metric has a detection rate of only 1.8%, the slope, double slope, and double delta metrics have detection rates between 50 and 51%, and the MuSDA and MuSD metrics have detection rates of 62.9% and 63.8%, respectively. In Case 8, zero-delay security code estimation and replay attacks are used. In this case, compared to those of Case 7, the double slope and ELP metrics still perform poorly, with detection rates of approximately 0, and the detection rates of the slope and ratio metrics decrease by 13.6% and 13.1%, respectively. The detection rates of the double slope, double delta, MuSDA, and MuSD metrics remain approximately unchanged, with MuSD showing the best detection rate of 63.3%.

Table 6 Summary of detection rates for different metrics based on the TEXBAT dataset.

Overall, among the eight metrics considered in the experiments, the MuSD and MuSDA obtained the best detection performance, showing the highest detection rates in all the experiments. The ratio and slope metrics showed the next best detection performance; although their detection capability was not as good as that of the MuSD and MuSDA metrics, they obtained good detection rates in all the cases. In contrast, the double delta, double slope, delta, and ELP metrics performed poorly, with detection rates close to 0 in some cases. The reason is that MuSD and MuSDA exploit advantages including the offset detection capability of complementary correlators, which comprehensively improves the detection capability of time-type and location-type spoofing signals, such as phase shifts, power suppression, and Earth-centered Earth-fixed coordinate deviations. It also solves the problem in that other metrics are not effective in detecting highly similar spoofing (the code phase, the carrier phase, and power are all very close), improving the spoof detection ability.

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